International Association for Cryptologic Research

International Association
for Cryptologic Research


Multi-key Homomorphic Signatures Unforgeable Under Insider Corruption

Russell W. F. Lai
Raymond K. H. Tai
Harry W. H. Wong
Sherman S. M. Chow
DOI: 10.1007/978-3-030-03329-3_16
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Presentation: Slides
Conference: ASIACRYPT 2018
Abstract: Homomorphic signatures (HS) allows the derivation of the signature of the message-function pair (m, g), where $$m = g(m_1, \ldots , m_K)$$, given the signatures of each of the input messages $$m_k$$ signed under the same key. Multi-key HS (M-HS) introduced by Fiore et al.  (ASIACRYPT’16) further enhances the utility by allowing evaluation of signatures under different keys. The unforgeability of existing M-HS notions assumes that all signers are honest. We consider a setting where an arbitrary number of signers can be corrupted, called unforgeability under corruption, which is typical for natural applications (e.g., verifiable multi-party computation) of M-HS. Surprisingly, there is a huge gap between M-HS (for arbitrary circuits) with and without unforgeability under corruption: While the latter can be constructed from standard lattice assumptions (ASIACRYPT’16), we show that the former likely relies on non-falsifiable assumptions. Specifically, we propose a generic construction of M-HS with unforgeability under corruption from zero-knowledge succinct non-interactive argument of knowledge (ZK-SNARK) (and other standard assumptions), and then show that such M-HS implies zero-knowledge succinct non-interactive arguments (ZK-SNARG). Our results leave open the pressing question of what level of authenticity and utility can be achieved in the presence of corrupt signers under standard assumptions.
  title={Multi-key Homomorphic Signatures Unforgeable Under Insider Corruption},
  booktitle={Advances in Cryptology – ASIACRYPT 2018},
  series={Lecture Notes in Computer Science},
  author={Russell W. F. Lai and Raymond K. H. Tai and Harry W. H. Wong and Sherman S. M. Chow},